On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / / Mark Green, Phillip A. Griffiths.
In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory...
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Green, Mark, author. aut http://id.loc.gov/vocabulary/relators/aut On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / Mark Green, Phillip A. Griffiths. Course Book Princeton, NJ : Princeton University Press, [2004] ©2005 1 online resource (208 p.) : 10 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 157 Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n = 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Zn(X) -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ2(X) for X an Algebraic Surface -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) MATHEMATICS / Algebra / Abstract. bisacsh Addition. Algebraic K-theory. Algebraic character. Algebraic curve. Algebraic cycle. Algebraic function. Algebraic geometry. Algebraic number. Algebraic surface. Algebraic variety. Analytic function. Approximation. Arithmetic. Chow group. Codimension. Coefficient. Coherent sheaf cohomology. Coherent sheaf. Cohomology. Cokernel. Combination. Compass-and-straightedge construction. Complex geometry. Complex number. Computable function. Conjecture. Coordinate system. Coprime integers. Corollary. Cotangent bundle. Diagram (category theory). Differential equation. Differential form. Differential geometry of surfaces. Dimension (vector space). Dimension. Divisor. Duality (mathematics). Elliptic function. Embedding. Equation. Equivalence class. Equivalence relation. Exact sequence. Existence theorem. Existential quantification. Fermat's theorem. Formal proof. Fourier. Free group. Functional equation. Generic point. Geometry. Group homomorphism. Hereditary property. Hilbert scheme. Homomorphism. Injective function. Integer. Integral curve. K-group. K-theory. Linear combination. Mathematics. Moduli (physics). Moduli space. Multivector. Natural number. Natural transformation. Neighbourhood (mathematics). Open problem. Parameter. Polynomial ring. Principal part. Projective variety. Quantity. Rational function. Rational mapping. Reciprocity law. Regular map (graph theory). Residue theorem. Root of unity. Scientific notation. Sheaf (mathematics). Smoothness. Statistical significance. Subgroup. Summation. Tangent space. Tangent vector. Tangent. Terminology. Tetrahedron. Theorem. Transcendental function. Transcendental number. Uniqueness theorem. Vector field. Vector space. Zariski topology. Griffiths, Phillip A., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691120447 https://doi.org/10.1515/9781400837175 https://www.degruyter.com/isbn/9781400837175 Cover https://www.degruyter.com/document/cover/isbn/9781400837175/original |
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Green, Mark, Green, Mark, Griffiths, Phillip A., |
spellingShingle |
Green, Mark, Green, Mark, Griffiths, Phillip A., On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n = 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Zn(X) -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ2(X) for X an Algebraic Surface -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index |
author_facet |
Green, Mark, Green, Mark, Griffiths, Phillip A., Griffiths, Phillip A., Griffiths, Phillip A., |
author_variant |
m g mg m g mg p a g pa pag |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Griffiths, Phillip A., Griffiths, Phillip A., |
author2_variant |
p a g pa pag |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Green, Mark, |
title |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / |
title_full |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / Mark Green, Phillip A. Griffiths. |
title_fullStr |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / Mark Green, Phillip A. Griffiths. |
title_full_unstemmed |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / Mark Green, Phillip A. Griffiths. |
title_auth |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / |
title_alt |
Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n = 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Zn(X) -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ2(X) for X an Algebraic Surface -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index |
title_new |
On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / |
title_sort |
on the tangent space to the space of algebraic cycles on a smooth algebraic variety. (am-157) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2004 |
physical |
1 online resource (208 p.) : 10 line illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Abstract -- Chapter One. Introduction -- Chapter Two. The Classical Case When n = 1 -- Chapter Three. Differential Geometry of Symmetric Products -- Chapter Four. Absolute Differentials (I) -- Chapter Five Geometric Description of T̳Zn(X) -- Chapter Six. Absolute Differentials (II) -- Chapter Seven. The Ext-definition of TZ2(X) for X an Algebraic Surface -- Chapter Eight. Tangents to Related Spaces -- Chapter Nine. Applications and Examples -- Chapter Ten. Speculations and Questions -- Bibliography -- Index |
isbn |
9781400837175 9783110494914 9783110442502 9780691120447 |
url |
https://doi.org/10.1515/9781400837175 https://www.degruyter.com/isbn/9781400837175 https://www.degruyter.com/document/cover/isbn/9781400837175/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516.35 |
dewey-sort |
3516.35 |
dewey-raw |
516.35 |
dewey-search |
516.35 |
doi_str_mv |
10.1515/9781400837175 |
oclc_num |
979577405 |
work_keys_str_mv |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) / |
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